**DDA2001, April2001**

*Session 2. Very Big Things*

Monday, 1:30-3:40pm
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## [2.04] Spectral Analysis of Orbits

*C. Hunter (Florida State University)*

Building galactic models requires the use of a large number
of orbits, and so is helped by rapid ways of obtaining
accurate descriptions of them. Regular orbits lie on 3-tori
in phase space, are quasi-periodic with three fundamental
frequencies, and can be described by triple Fourier series.
The triple Fourier series are strongly constrained by the
Hamiltonian nature of the problem, because they are
derivable from the scalar generating function which gives
the canonical transformation to action-angle variables.
Orbital symmetries are reflected in the special structure of
their Fourier series. This talk will discuss efficient ways
of using all the phase space information available from
numerical integrations of orbits to derive their Fourier
series. Once the Fourier series are known, orbital densities
can be derived directly from them (Copin, Zhao, & de Zeeuw
2000).

This work has been supported by NSF through grant
DMS-9704615.

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